Image being duplicated as a result of modification in local.css

Have a situation wherein I want to indent items in a ul, li and who also have the h3 tag. I've modified the local.css file with the following:

ul li h3 {
background:transparent url(images/green-bullet.png) no-repeat scroll left;
list-style-image:none;
list-style-type:none;
padding-left:1.666em;
}

as a result I get two of the green-bullet.png images, I'm sure this is because I've listed it as background:transparent url(images/green-bullet.png) no-repeat scroll left; and because it also exists in the style.css file be default. I've attached a screenshot snippet of the ul w/ the error.

I'm not sure how to eliminate the first green-bullet.png so only the one listed in the local.css file will show.

Would appreciate any help.

Thanks